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How to draw tropical planes.

Herrmann, Sven, Jensen, Anders, Joswig, Michael, Sturmfels, Bernd (2009)

The Electronic Journal of Combinatorics [electronic only]

Hyperbolische Transformation konvexer Polyeder

Ralf Gollmer (1981)

Aplikace matematiky

Der Artikel beschäftigt sich mit einigen Eigenschaften von hyperbolischen, d. h. gebrochen-affinen, Transformationen, welche für die Bilder konvexer Polyeder bei solchen Transformationen von Bedeutung sind. Es wird eine explizite Darstellung des Bildes eines konvexen Polyeders durch Ecken und Kanten des Urbildpolyeders gewonnen, die Konvexität des Bildes und das Bild des relativen Inneren einer konvexen Menge untersucht.

Hyperideal polyhedra in hyperbolic 3-space

Xiliang Bao, Francis Bonahon (2002)

Bulletin de la Société Mathématique de France

A hyperideal polyhedron is a non-compact polyhedron in the hyperbolic 3 -space 3 which, in the projective model for 3 ℝℙ 3 , is just the intersection of 3 with a projective polyhedron whose vertices are all outside 3 and whose edges all meet 3 . We classify hyperideal polyhedra, up to isometries of 3 , in terms of their combinatorial type and of their dihedral angles.

Isocanted alcoved polytopes

María Jesús de la Puente, Pedro Luis Clavería (2020)

Applications of Mathematics

Through tropical normal idempotent matrices, we introduce isocanted alcoved polytopes, computing their f -vectors and checking the validity of the following five conjectures: Bárány, unimodality, 3 d , flag and cubical lower bound (CLBC). Isocanted alcoved polytopes are centrally symmetric, almost simple cubical polytopes. They are zonotopes. We show that, for each dimension, there is a unique combinatorial type. In dimension d , an isocanted alcoved polytope has 2 d + 1 - 2 vertices, its face lattice is the lattice...

Isometric Embeddings of Pro-Euclidean Spaces

Barry Minemyer (2015)

Analysis and Geometry in Metric Spaces

In [12] Petrunin proves that a compact metric space X admits an intrinsic isometry into En if and only if X is a pro-Euclidean space of rank at most n, meaning that X can be written as a “nice” inverse limit of polyhedra. He also shows that either case implies that X has covering dimension at most n. The purpose of this paper is to extend these results to include both embeddings and spaces which are proper instead of compact. The main result of this paper is that any pro-Euclidean space of rank...

Isoperimetric Regions in Rnwith Density rp

Wyatt Boyer, Bryan Brown, Gregory R. Chambers, Alyssa Loving, Sarah Tammen (2016)

Analysis and Geometry in Metric Spaces

We show that the unique isoperimetric regions in Rn with density rp for n ≥ 3 and p > 0 are balls with boundary through the origin.

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